A Complex System View of Why Stock Markets Crash

Abstract: The young science of complexity, which studies systems as
diverse as the human body, the earth and the universe, offers novel insights
on the question raised in the title. The science of complexity explains large-scale
collective behavior, such as well-functioning capitalistic markets, and also
predicts that financial crashes and depressions are intrinsic properties resulting
from the repeated nonlinear interactions between investors. Applying concepts
and methods from complex theory and statistical physics, we have developed
mathematical measures to successfully predict the emergence and development
of speculative bubbles as well as depressions. This essay attempts to capture
and extend the essence of the book with the same title published in January
2003 by Princeton University Press. Recent novelties and live predictions are
available at http://www.ess.ucla.edu/faculty/sornette/

Complexity theory: what, why and how?

The history of complexity goes back to antiquity, Greece, China and beyond.
Complexity was mostly thought of as being characterized by somehow going beyond
what human minds can handle. The idea of complexity as a coherent scientific
concept is quite new and dates back to the early 1960s with efforts to define
computational complexity in the development of modern computers. The issue
of computational complexity arose naturally with the need to measure the resources,
time and memory as a function of the size and nature of the input problem to
solve. The concept of complexity is also attached to the impossibility theorems
of Godel and other mathematicians developed in the 1930s and later dealing
with the sizes of axioms for logical theories, and with numbers of ways to
satisfy such axioms. The idea that complexity might also be related to information
content was also developed with the notion of algorithmic information content
as the length of a shortest program to represent a given system. A new wave
of interest spurred with the involvement of physicists who discovered in the
early 1980s that complexity might offer a general guideline to understand the
physical, biological as well as social worlds [Wolfram, 2002].

The study of out-of-equilibrium dynamics (e.g. dynamical phase transitions)
and of heterogeneous systems (e.g. glasses, rocks) has progressively made popular
in physics and then in its sisters branches (geology, biology, etc.) the concept
of complex systems and the importance of systemic approaches: systems with
a large number of mutually interacting parts, often open to their environment,
self-organize their internal structure and their dynamics with novel and sometimes
surprising macroscopic "emergent" properties.

The complex system approach, which involves seeing inter-connections and relationships,
i.e., the whole picture as well as the component parts, is nowadays pervasive
in modern control of engineering devices and business management. It is also
plays an increasing role in most of the scientific disciplines, including biology
(biological networks, ecology, evolution, origin of life, immunology, neurobiology,
molecular biology, etc), geology (plate-tectonics, earthquakes and volcanoes,
erosion and landscapes, climate and weather, environment, etc.), economy and
social sciences (including cognition, distributed learning, interacting agents,
etc.). There is a growing recognition that progress in most of these disciplines,
in many of the pressing issues for our future welfare as well as for the management
of our everyday life will need such a systemic complex system and multidisciplinary
approach.

A central property of a complex system is the possible occurrence of coherent
large-scale collective behaviors with a very rich structure, resulting from
the repeated non-linear interactions among its constituents: the whole turns
out to be much more than the sum of its parts. It is widely believed that most
of these systems are not amenable to mathematical, analytic descriptions and
can only be explored by means of "numerical experiments." In the
context of the mathematics of algorithmic complexity [Chaitin, 1987], most
complex systems are said to be computationally irreducible, i.e., the only
way to decide about their evolution is to actually let them evolve in time.
Accordingly, the future time evolution of complex systems would be inherently
unpredictable. This unpredictability does not prevent however the application
of the scientific method for the prediction of novel. In contrast, it refers
to the frustration to satisfy the curiosity, strengthened by the anguish and
hope that humans have always projected on their future. Is modern science really
putting out of reach the grail of predicting (some of) the future evolution
of complex systems?

This view has recently been defended persuasively in concrete prediction applications,
such as the socially important issue of earthquake prediction (see the contributions
in [Nature debate, 1999]. In addition to the persistent failures at reaching
a reliable earthquake predictive scheme, this view is rooted theoretically
in the analogy between earthquakes and self-organized criticality [Bak, 1996].
In this "fractal" framework, there is no characteristic scale and
the power law distribution of sizes reflects the fact that the large earthquakes
are nothing but small earthquakes that did not stop. They are thus unpredictable
because their nucleation is not different from that of the multitude of small
earthquakes which obviously cannot be all predicted.

Does this really hold for all features of complex systems? Take our personal
life. We are not really interested in knowing in advance at what time we will
go to a given store or drive in a highway. We are much more interested in forecasting
the major bifurcations ahead of us, involving the few important things, like
health, love and work that count for our happiness. Similarly, predicting the
detailed evolution of complex systems has no real value and the fact that we
are taught that it is out of reach from a fundamental point of view does not
exclude the more interesting possibility to predict phases of evolutions of
complex systems that really count.

It turns out that most complex systems around us do exhibit rare and sudden
transitions, that occur over time intervals that are short compared to the
characteristic time scales of their posterior evolution. Such extreme events
express more than anything else the underlying "forces" usually hidden
by almost perfect balance and thus provide the potential for a better scientific
understanding of complex systems. These crises have fundamental societal impacts
and range from large natural catastrophes, catastrophic events of environmental
degradation, to the failure of engineering structures, crashes in the stock
market, social unrest leading to large-scale strikes and upheaval, economic
drawdowns on national and global scales, regional power blackouts, traffic
gridlock, diseases and epidemics, etc. It is essential to realize that the
long-term behavior of these complex systems is often controlled in large part
by these rare catastrophic events: the universe was probably born during an
extreme explosion (the "big-bang"); the nucleosynthesis of most important
atomic elements constituting our matter results from the colossal explosion
of supernovae; the largest earthquake in California repeating about once every
two centuries accounts for a significant fraction of the total tectonic deformation;
landscapes are more shaped by the "millennium" flood that moves large
boulders rather than the action of all other eroding agents; the largest volcanic
eruptions lead to major topographic changes as well as severe climatic disruptions;
evolution is characterized by phases of quasi-statis interrupted by episodic
bursts of activity and destruction; financial crashes can destroy in an instant
trillions of dollars; political crises and revolutions shape the long-term
geopolitical landscape; even our personal life is shaped on the long run by
a few key decisions and happenings.

The outstanding scientific question is thus how such large-scale patterns
of catastrophic nature might evolve from a series of interactions on the smallest
and increasingly larger scales. In complex systems, it has been found that
the organization of spatial and temporal correlations do not stem, in general,
from a nucleation phase diffusing across the system. It results rather from
a progressive and more global cooperative process occurring over the whole
system by repetitive interactions. An instance would be the many occurrences
of simultaneous scientific and technical discoveries signaling the global nature
of the maturing process.

Standard models and simulations of scenarios of extreme events are subject
to numerous sources of error, each of which may have a negative impact on the
validity of the predictions [Karplus, 1992]. Some of the uncertainties are
under control in the modeling process; they usually involve trade-offs between
a more faithful description and manageable calculations. Other sources of errors
are beyond control as they are inherent in the modeling methodology of the
specific disciplines. The two known strategies for modeling are both limited
in this respect: analytical theoretical predictions are out of reach for most
complex problems. Brute force numerical resolution of the equations (when they
are known) or of scenarios is reliable in the "center of the distribution," i.e.,
in the regime far from the extremes where good statistics can be accumulated.
Crises are extreme events that occur rarely, albeit with extraordinary impact,
and are thus completely under-sampled and thus poorly constrained. Even the
introduction of teraflop (or even pentaflops in the futur) supercomputers does
not change qualitatively this fundamental limitation.

Recent developments suggest that non-traditional approaches, based on the
concepts and methods of statistical and nonlinear physics coupled with ideas
and tools from computation intelligence could provide novel methods in complexity
to direct the numerical resolution of more realistic models and the identification
of relevant signatures of impending catastrophes. Enriching the concept of
self-organizing criticality, the predictability of crises would then rely on
the fact that they are fundamentally outliers, e.g. large earthquakes are not
scaled-up versions of small earthquakes but the result of specific collective
amplifying mechanisms. Similarly, financial crashes do not belong to the same
distribution as smaller market moves [Johansen and Sornette, 2002]. To address
this challenge posed by the identification and modeling of such outliers, the
available theoretical tools comprise in particular bifurcation and catastrophe
theories, dynamical critical phenomena and the renormalization group, nonlinear
dynamical systems, and the theory of partially (spontaneously or not) broken
symmetries. Some encouraging results have been gathered on concrete problems,
such as the prediction of the failure of complex engineering structures, the
detection of precursors to stock market crashes and of human parturition, with
exciting potential for earthquakes [Sornette, 2002].

We now proceed to present how these ideas have been explored and exploited
in the financial and social spheres.

Questions and lessons from the stock Market Crach of October 1987

From the opening on October 14, 1987 through the market close on October 19,
major indexes of market valuation in the United States declined by 30 percent
or more. Furthermore, all major world markets declined substantially in the
month, which is itself an exceptional fact that contrasts with the usual modest
correlations of returns across countries and the fact that stock markets around
the world are amazingly diverse in their organization (Barro et al., 1989,
White, 1996).

The crash of October, 1987 and its black monday on October, 19 remains one
of the most striking drops ever seen on stock markets, both by its overwhelming
amplitude and its encompassing sweep over most markets worldwide. It was preceded
by a remarkably strong "bull" regime epitomized by the following
quote from Wall Street Journal, August 26, 1987, the day after the 1987 market
peak: "In a market like this, every story is a positive one. Any news
is good news. It's pretty much taken for granted now that the market is going
to go up." This and other indicators, such as the implied volatility,
indicate that investors were thus mostly unaware of the forthcoming risk happenings
(Grant, 1990).

A lot of work has been carried out to unravel the origin(s) of the crash,
notably in the properties of trading and the structure of markets; however,
no clear cause has been singled out. It is noteworthy that the strong market
decline during October 1987 followed what for many countries had been an unprecedented
market increase during the first nine months of the year and even before. In
the US market, for instance, stock prices advanced 31.4 % over those nine months.
Some commentators have suggested that the real cause of October's decline was
that over-inflated prices generated a speculative bubble during the earlier
period. The main explanations that have been invoked include computer trading,
derivative securities, lack of liquidity, trade and budget deficits, overvaluation,
etc. Other cited potential causes involve the auction system itself, the presence
or absence of limits on price movements, regulated margin requirements, off-market
and off-hours trading (continuous auction and automated quotations), the presence
or absence of floor brokers who conduct trades but are not permitted to invest
on their own account, the extent of trading in the cash market versus the forward
market, the identity of traders (i.e. institutions such as banks or specialized
trading firms), the significance of transaction taxes, etc.

More rigorous and systematic analyses on univariate associations and multiple
regressions of these various factors conclude that it is not at all clear what
caused the crash (Barro et al., 1989). The most precise statement, albeit somewhat
self-referential, is that the most statistically significant explanatory variable
in the October crash can be ascribed to the normal response of each country's
stock market to a worldwide market motion. A world market index was thus constructed
by equally weighting the local currency indexes of the 23 major industrial
countries mentioned above and normalized to 100 on september 30, 1987 (Barro
et al., 1989). It fell to 73.6 by October 30. The important result is that
it was found to be statistically related to monthly returns in every country
during the period from the beginning of 1981 until the month before the crash,
albeit with a wildly varying magnitude of the responses across countries. This
correlation was found to swamp the influence of the institutional market characteristics.
This signals the possible existence of a subtle but nonetheless influential
world-wide cooperativity (contagion) at times preceding crashes.

According to this view, the crash of a given country's market is "explained" as
driven by or responding to a world-wide market crash. But what is the origin
of the world market crash itself? Is it the result of the superposition of
all individual national crashes? This line of argument is reminiscent of the
infamous chicken-and-egg problem and we believe that it does not reply adequately
to the question posed in the title.

Questions and lessons from the stock Market Crach of March-April 2002 on
the Nasdaq index

With the low of 3227 on April, 17, 2000, the Nasdaq Composite Index lost over
37% of its all-time high of 5133 reached on the 10th of March 2000. The Nasdaq
Composite consists mainly of stock related to the so-called "New Economy," i.e.,
the Internet, software, computer hardware, telecommunication and so on. A main
characteristic of these companies is that their price-earning-ratios (P/E's),
and even more so their price-dividend-ratios, often came in three digits .
Opposed to this, so-called "Old Economy" companies, such as Ford,
General Motors and Daimler-Chrysler, had P/E's of the order of 10. The difference
between Old Economy and New Economy stocks was thus the expectation of future
earnings: investors expected an enormous increase in for example the sale of
Internet and computer related products rather than in car sales and were hence
more willing to invest in Cisco rather than in Ford notwithstanding the fact
that the earning-per-share of the former is much smaller than for the later.

In the standard fundamental valuation formula, in which the expected return
of a company is the sum of the dividend return and of the growth rate, New
Economy companies are supposed to compensate for their lack of present earnings
by a fantastic potential growth. In essence, this means that the bull market
observed in the Nasdaq until the end of the first quarter of 2000 was fueled
by expectations of increasing future earnings rather than economic fundamentals:
the price-to-dividend ratio for a company such as Lucent Technologies (LU)
with a capitalization of over 300 billions prior to its crash on the 5 January
2000 was over 900 which means that you got a higher return on your checking
account(!) unless the price of the stock increases. Opposed to this, an Old
Economy company such as DaimlerChrysler gives a return which is more than thirty
times higher. Nevertheless, the shares of Lucent Technologies rose by more
than 40% during 1999 whereas the share of DaimlerChrysler declined by more
than 40% in the same period.

The generic scenario

This makes clear that it is the expectation of future earnings rather than
present economic reality that motivates the average investor, with the potential
for the creation of a speculative bubble. History provides many examples of
bubbles driven by unrealistic expectations of future earnings followed by crashes.
The same basic ingredients are found repeatedly. Markets go through a series
of stages, beginning with a market or sector that is successful, with strong
fundamentals. Credit expands, and money flows more easily. (Near the peak of
Japan's bubble in 1990, Japan's banks were lending money for real estate purchases
at more than the value of the property, expecting the value to rise quickly.)
As more money is available, prices rise. More investors are drawn in, and expectations
for quick profits rise. The bubble expands, and then bursts. In other words,
fueled by initially well-founded economic fundamentals, investors develop a
self-fulfilling enthusiasm by an imitative process or crowd behavior that leads
to the building of castles in the air, to paraphrase Malkiel (1990).

Furthermore, the causes of the crashes on the US markets in 1929, 1987, 1998
and in 2000 belongs to the same category, the difference being mainly in which
sector the bubble was created: in 1929, it was utilities; in 1987, the bubble
was supported by a general deregulation of the market with many new private
investors entering the market with very high expectations with respect to the
profit they would make; in 1998, it was an enormous expectation to the investment
opportunities in Russia that collapsed; before 2000, it was the extremely high
expectations to the Internet, telecommunication etc. that fueled the bubble.

Positive feedback, collective behaviors and herding

In a culmination of more than ten years of research on the science of complex
system, we have thus challenged the standard economic view that stock markets
are both efficient and unpredictable. The main concepts that are needed to
understand stock markets are imitation, herding, self-organized cooperativity
and positive feedbacks, leading to the development of endogenous instabilities.
According to this theory, local effects such as interest raises, new tax laws,
new regulations and so on, invoked as the cause of the burst of a given bubble
leading to a crash, are only one of the triggering factors but not the fundamental
cause of the bubble collapse. We propose that the true origin of a bubble and
of its collapse lies in the unsustainable pace of stock market price growth.
As a speculative bubble develops, it becomes more and more unstable and very
susceptible to any disturbance.

Large stock market crashes are thus the social analogs of so-called critical
points studied in the statistical physics community in relation to magnetism,
melting, and other phase transformation of solids, liquids and gas (Sornette,
2000). This theory is based on the existence of an (unwilling) cooperative
behavior of traders imitating each other which leads to progressively increasing
build-up of market cooperativity, or effective interactions between investors,
often translated into accelerating ascent of the market price over months and
years before the crash. According to this theory, the specific manner by which
prices collapsed is not the most important problem: a crash occurs because
the market has entered an unstable phase and any small disturbance or process
may have triggered the instability.

Think of a ruler held up vertically on your finger: this very unstable position
will lead eventually to its collapse, as a result of a small (or absence of
adequate) motion of your hand or due to any tiny whiff of air. The collapse
is fundamentally due to the unstable position; the instantaneous cause of the
collapse is secondary. In the same vein, the growth of the sensitivity and
the growing instability of the market close to such a critical point might
explain why attempts to unravel the local origin of the crash have been so
diverse. Essentially, anything would work once the system is ripe. In this
view, a crash has fundamentally an endogenous, or internal origin and exogenous,
or external shocks only serve as triggering factors.

Recent academic research in the field of complex systems suggest that the
economy as well as stock markets self-organize under the competing influences
of positive and negative feedback mechanisms. Positive feedbacks, i.e., self-reinforcement,
refer for instance to the fact that, conditioned on the observation that the
market has recently moved up (respectively down), this makes it more probable
to keep it moving up (respectively down), so that a large cumulative move may
ensue. "Positive feedback" is the opposite of "negative feedback," the
latter being a concept well-known for instance in population dynamics in the
presence of scarce resources. Rational markets and stable economic equilibrium
derive from the forces of negative feedback. When positive feedback forces
dominate, deviations from equilibrium lead to crises. Such instabilities can
be seen as intrinsic endogenous progenies of the dynamical organization of
the system.

Positive feedbacks lead to collective behavior, such as herding in sells during
a financial crash. This collective behavior does not require the coordination
of people to take the same action but results from the convergence of selfish
interests together with the impact of interactions between people through the
complex network of their acquaintances. Complex system theory tells us that
such collective behaviors may be very robust against external intervention,
as along as the selfish individualistic nature of individual so-called utility
function dominates. The collective is robust because it derives from a bottom-up
mechanism. Similar resilience is observed for instance in the Internet for
instance due to its delocalized structure and self-organization.

As a consequence, the origin of crashes is much more subtle than often thought,
as it is constructed progressively by the market as a whole, as a self-organizing
process. In this sense, the true cause of a crash could be termed a systemic
instability. This leads to the possibility that the market anticipates the
crash in a subtle self-organized and cooperative fashion, hence releasing precursory "fingerprints" observable
in the stock market prices (Sornette and Johansen, 2001; Sornette, 2003). These "fingerprints" have
been modeled by "log-periodically decorated power laws" (LPPL), which
are beautiful mathematical patterns associated with the mathematical generalization
of the notion of fractals to complex imaginary dimensions (Sornette, 1998).
We refer to the book (Sornette, 2003) for a detailed description and the review
of many empirical tests and of several forward predictions. In particular,
we predicted in January 1999 that Japan's Nikkei index would rise 50 percent
by the end of that year, at a time when other economic forecasters expected
the Nikkei to continue to fall, and when Japan's economic indicators were declining.
The Nikkei rose more than 49 percent during that time. We also successfully
predicted several short-term changes of trends in the US market and in the
Nikkei. Or course, we are not able to predict stock markets with anything close
to 100 percent accuracy - just as weather forecasting cannot say with absolute
certainty what the weekend weather will be - but our predictions will become
more accurate as we refine our methods.

Our theory of collective behavior predicts robust signatures of speculative
phases of financial markets, both in accelerating bubbles and decreasing prices
(see below). These precursory patterns have been documented for essentially
all crashes on developed as well as emergent stock markets. Accordingly, the
crash of October, 1987 is not unique but a representative of an important class
of market behavior, underlying also the crash of October 1929 (Galbraith, 1997)
and many others (Kindleberger, 2000; Sornette, 2003).

Stock market crashes are often unforeseen by most people, especially economists.
One reason why predicting complex systems is difficult is that we have to look
at the forest rather than the trees, and almost nobody does that. Our approach
tries to avoid that trap. From the tulip mania, where tulips worth tens of
thousands of dollars in present U.S. dollars became worthless a few months
later, to the U.S. bubble in 2000, the same patterns occur over the centuries.
Today we have electronic commerce, but fear and greed remain the same. Humans
remained endowed with basically the same qualities today as they were in the
17th century.

It is often thought that the efficiency of the market acquired by the diligence
of greedy investors makes impossible the existence of predictability: as soon
as a pattern is detected, if profitable, it should disappear by the action
of arbitragers. This common wisdom is correct for most patterns. However, there
are some structures, such as the LPPL, which result from positive feedbacks.
Hence, the more people believe in such patterns, the more their action will
be in line and will reinforce them. This idea is incorporated in our theory
of rational expectation bubbles [Johansen et al., 1999; 2000].

"Antibubbles" in Japan and the US and World markets

Imitation between investors and their herding behavior not only lead to speculative
bubbles with accelerating overvaluations of financial markets possibly followed
by crashes, but also to "antibubbles" with decelerating market devaluations
following market peaks (Johansen and Sornette, 1999), that can be modeled by
the same type of "log-periodically decorated power law" decay found
for accelerating bubbles. There is thus a certain degree of symmetry between
the speculative behavior of the "bull" and "bear" market
regimes. The concept of an "anti-bubble", that we coined to stress
the fact that positive feedbacks are also at work in decreasing markets, is
an adaptation of the concept of anti-particle in particle physics, such as
the positron which is the positively charged particle exactly symmetric to
the negatively charged electron. This concept stresses the symmetry between
bubbles and anti-bubbles.

We have studied in details several anti-bubbles, the prominent example being
the Japanese Nikkei stock index since January 1, 1990. Other examples include
gold after1980. Both after their all-time highs (Johansen and Sornette, 1999).
The Japanese antibubble from 1990 to present is all the more interesting because
we published a prediction in January 1999 of the behavior of the Japanese stock
market in the following two years that have been remarkably successful (Johansen
and Sornette, 2000; Sornette, 2003). The fulfillment of this prediction is
quite remarkable because it included a change of trend: at the time when the
prediction was issued, the market was declining and showed no tendency to increase.
Many economists were at that time very pessimistic and could not envision when
Japan and its market would rebound. Not only did we correctly predicted a rebound
of 50% for the end of 1999 but they also foresaw another change of trend at
the beginning of 2000. The approval in Oct., 1998 by the Japanese parliament
of legislation to allow the government to nationalize failing banks and to
commit more than $US 500 billion to rescue the nation's banking system led
to a short revival of Japan's economy however bought at the expense of more
than $1US trillion in government spending in a series of economic stimulus
packages that included numerous public works projects. Sornette (2003) develops
further this question and reports all cases, successes and failures of past
predictions in several different markets.

The situation of Japan in 1992 is no more very different from that of the
US after the burst of the "new economy" bubble in March-April 2000
and the cascade of discoveries (which will probably never be fully unveiled
in their full extent) of creative accounting of companies striving to look
good in the eyes of analysts rather than to build strong fundamentals. The
growing appreciation in 2002 of the crisis in the American financial system
is reminiscent of the starting point of Japan's massive financial bubble burst
more than 10 years before and of the inter-twinning of the bad debts and bad
performance of banks whose capital is invested in the shares of other banks,
thus creating the potential for a catastrophic cascade of bankruptcies. Japan
has rediscovered before the US the faults of the 19th century financial system
in the US in which stock markets were so much intertwined with their overall
banking financial system, that busts and bursts occurred more than once every
decade, with firms losing their credit lines and workers and consumers their
savings and often their employment. It is often said that the 1930s depression
was the last of the stock market and bank-induced economic collapses. The growing
fuzziness between financial banking systems and stock markets, in part due
to the innovations in information technology, has re-created the climate for
stronger bubbles.

The big problem is that, in the collapse following them, policy interventions
such as lowering interest rates, reducing taxes, and government spending packages
may be much less effective, due to several mechanism such as the so-called
liquidity trap, a process in which government and the central bank policy becomes
essentially useless due to an effective vanishing short-term interest rate,
or due to lack of consumer confidence who reduce their consumption and spending.
Often forgotten within macroeconomics policies, the human aspect of the problem
has to be fully appreciated: for instance, how to restore the confidence of
Japanese households into a brighter future so that they resume spending and
innovating even more rather than saving too much. Saving is a natural reaction
to losses but may accentuate the problem by the process of "positive feedback." We
argue that standard macro-economic reasoning will not be sufficient as long
as one forgets the possible stable and unstable regime shifts resulting from
the emergence of collective behaviors of imitation and herding, which themselves
emphasize a strongly non-linear dynamical view point in order to understand
economies and stock markets.

Recently, we have applied our theory and its derived methodology to the US
since the burst of the last 'new economy' bubbles in 2000 (Sornette and Zhou,
2002) as well as to many other western and emergent markets in the world (Zhou
and Sornette, 2002). We find the same characteristic signature of an anti-bubble
regime that started almost synchronously in most westerm markets in August
2000. As of September 2002, we also issued a prediction for the next two years
for the US stock market: the S&P500 US index should continue its up-trend
for no more than a few months and then resume a descent extending well in the
first semester of 2004 with an amplitude of more than 20%. This prediction
can be considered to be refinement of a longer term analysis combining three
pieces of empirical evidence (Johansen and Sornette, 2001), namely human population,
gross national product worldwide and stock market indices, which suggest all
together a fundamental turning point in the growth of the economic impact of
mankind in the decades ahead of us. In addition, a prediction is made that
starting around 1999, a 5 to 10 years consolidation of international stock
markets will occur, allowing a purge after the over-aggressive appetite of
the preceding decade (Sornette, 2003). Since 2000, this prediction has been
born out.

Generalization to other markets: Is a Real Estate Bubble Ready to Burst?

Following the collapse of the "new economy" bubble of 2000, the
Federal Reserve aggressively lowered its discount rate from 6.5 to 1.25 percent
in less than two years in an attempt to coax a stronger recovery of the U.S.
economy. But, there is growing apprehension that this rate reduction is creating
a new bubble in real estate, as historically low mortgage rates fuel strong
housing demand. Are we going from Charybdis to Scylla? This question is all
the more excruciating at a time when many other indicators suggest a significant
deflationary risk.

The young science of complexity, which studies systems as diverse as the human
body , the earth and the universe, offers novel insights on this troubling
question. As we already mentioned, this approach led us to predict the recovery
of the Japanese Nikkei in 1999 by 50 percent, to detect a speculative "anti-bubble" in
the U.S. stock market and worldwide since the summer of 2000 with a degree
of synchronicity never observed before and, recently, to predict that the U.S.
stock market will continue to weaken until the summer of 2004.

Stock market losses have destroyed as much as $5 trillion in investor wealth
since the market's peak in 2000. Fortunately, this has led to relatively minor
effects on the economy: the gross domestic product (GDP) exhibited a descent
of about one-half percent, a drop that would have been far worse without a
strong real estate sector.

While the economy has generally been contracting in the last two years, real
estate has been growing: house prices have been rising at a rate of about 2
per cent a year faster than income gains. Real consumer outlays and spending
on residential construction each rose about 3 percent during 2001. One of the
reasons for the relatively minor impact of the stock market losses may be found
in the offsetting effect in the real estate market. Home equity has gained
about $1.7 trillion in the same period, according to the chief economist for
the biggest U.S. mortgage firm, Fannie Mae. Since, according to the Federal
Reserve, home values have twice the impact on consumer spending that stock
values have via the "richness effect,"' the housing boom has offset
almost two-thirds of the stock market losses on the economy.

What is the risk for a real estate crash? Federal Reserve Chairman A. Greenspan
and Governor D.L. Kohn dismissed recently the possibility of a crash and do
not see any problem with the current real estate boom. Many others believe
they have detected a real estate bubble in the U.S. Statistics released every
month confirm that "the housing sector continues to defy all odds," in
the words of the chief economist for the National Association of Realtors,
David Lereah. American mortgages are on the path of becoming the single largest
class of fixed income securities on the planet. Total mortgage debt outstanding
has risen sharply during the last decade. While the total was about $2.7 trillion
in the first quarter of 1990, by the fourth quarter of 1999, it had almost
doubled, to $5.2 trillion. As a comparison, the total amount of cumulative
borrowing by the Federal Treasury, the national debt, was about $5.7 trillion
in August 2000.

Add to these elements that the demand for mortgage borrowing outstrips aggregate
domestic saving which is currently negative and has reached the lowest level
since record keeping began in 1959. This negative saving rate combined with
the continuing rapid growth of mortgage borrowing implies that there must be
a reduction in non-mortgage lending or an increase in fund flows from abroad
or both. This may lead to increased instability through globalization, resulting
from the behavior of international investors.

To make matters even worse, the real estate bubble is part of a general huge
credit "bubble" that has developed steadily over recent decades,
which includes the various U.S. federal money supply, and the personal, municipal,
corporate and federal debts (estimated by some to add up to as much as several
tens of trillions of dollars), which may not only drag down the recovery of
the economy but also lead to vulnerability to exogenous crises.

What is the risk of a real estate crash according to the science of complexity?
As we have already mentioned, recent research in the field of complex systems
suggest that the economy, as well as stock markets, self-organize under the
competing influences of positive and negative feedback mechanisms, such as
momentum investing in stock markets. Positive feedbacks lead to such collective
behavior as herding in buys during the growth of bubbles and sells during a
crash. Using this theory and its specification in the mathematics of fractals,
we have been searching for specific mathematical signatures of bubbles (Zhou
and Sornette, 2003). Speculative bubbles are observed in all assets at all
times and locations in history, from the tulip mania in Holland culminating
in 1636, to stocks, commodities, currency and real estate markets, in the past
and present. Our experience suggests that speculative bubbles have a rather
long characteristic gestation time, typically years.

Our analysis finds that the US real estate market is still far from an instability
and that there are no significant risks for a crash this year. The situation
is the opposite for the U.K. housing market as two unambiguous signatures show
that an unsustainable bubble started years even before the end of the stock
market bubble in 2000. These signatures have been found to be reliable predictors
of past crashes in financial markets.

The analysis points to the end of the bubble for the U.K. housing market no
later than the end of the year, with either a crash or a strong change of direction
in the UK housing market. While there are very strong correlations between
stock markets in developed countries at present, no such correlation has yet
materialized in real estate markets. In the longer term, however, investors
should remain watchful for indications of a possible spread to the U.S. real
estate market. Such signs would include an increase of correlation between
real estate markets and the growth of patterns similar to those found for the
UK real estate market.

Limitations of the log-periodic power law (LPPL) model

There are several important limitations to the predictability of markets,
when using the LPPL theory of herding.

(1) In order to be consistent with the self-correcting nature of markets,
crashes cannot be deterministically predictable but must contain stochastic
components. In our models, this is taken into account by realizing that we
are detecting only the growth or decay of a bubble, its climax, but this culmination
is not necessarily the time of the crash. The end of a bubble is the time when
the crash is the most probable. But a bubble may end in other ways than by
crashing, for instance by a smooth change of regime. There is always a non-zero
probability that the crash will not occur at all, a possibility that rationalizes
why investors may remain invested at times when markets grow in unsustainable
ways.

(2) A recent study combining ideas from critical phenomena, the impact of
agents' expectation, multi-scale analysis and the mathematical method of pattern
recognition of sparse data shows that the LPPL model detects more specifically
large changes of regimes rather than crashes per se [Sornette and Zhou, 2003].
This is a problem for practical applications dealing with hedging.

(3) Using the LPPL model, Johansen and Sornette [2003] have performed a systematic
classification of drawdowns in the two leading exchange markets (US dollar
against the Deutsmark and against the Yen), in the major world stock markets,
in the U.S. and Japanese bond market and in the gold market. They find that,
out of 49 significant outliers, 25 can be classified as endogenous (that is,
predictable with the LPPL theory), 22 as exogenous and 2 as associated with
the Japanese anti-bubble. Restricting to the world market indices, they find
31 outliers, of which 19 are endogenous, 10 are exogenous and 2 are associated
with the Japanese anti-bubble. The existence of exogenous crashes, that is,
genuine surprises that can move the market significantly, leads to an intrinsic
limitation of the predictability of crashes. This seems to be the unavoidable
lot of complex systems that are open to the outside, i.e., that are subjected
to a complicated flux of "news." The search for general and systematic
differences in the response of the stock market, for instance in the volatility
of prices, to endogenous versus exogenous shocks is described in [Sornette
and Helmstetter, 2003; Sornette et al., 2003].

Deflationary risk and a top-down extension of the collective behavior in
markets

A deflationary risk is looming over the US. Deflation could take huge proportions,
last years and cost a lot in terms of quality of life for many. With the unprecedented
debt levels of the US [Godley, 2003], it is probable that the familiar monetary
and fiscal remedies would fail. Indeed, a big problem is that policy interventions
such as lowering interest rates, reducing taxes, government spending packages
(including lavish war expenditures) and any measure to restore investors' confidence
may be much less effective than expected, as discovered with the Japanese so-called
liquidity trap, which is as we said a process in which government and the central
bank policy becomes essentially useless. In addition, loss of confidence by
investors may lead to a non-negligible cost to the overall economy, providing
a positive feedback reinforcing the bearish climate.

We suggest that what is needed to avoid or get out of deflation is for individual
countries to abandon the selfish policy of "Everyone for himself" that
is bound to blossom even further as the hardships unfold (such as trade wars,
protectionist backlash, dollar depreciation) in favor of a new approach where
the well-being of countries is considered collectively: the US economic problems
are the problems of the rest of the world (this is the implicit or explicit
standard US view point) but the economic problems of the rest of the world
are also US problems. Beyond lip service, this is a "new" view point
in the following sense: the US economic problems have no solution outside a
process in which the benefits (and drawbacks) attributed to policies followed
by country A incorporate also the benefits (and drawbacks) to the economy of
country B, and vice versa. Incorporating such an (apparently) unselfish component
in the assessment of policies seems like an hopeless chimera, in view for instance
of the difficulties of the European countries trying to achieve just that.
We contend that there are no other ways.

The argument is based again on the science of complexity, which studies the
emergence of organization in complex systems as diverse as the human body (biology),
the earth (geology) or the cosmos (astrophysics). This bottom-up mechanism
explains the robustness and strength of modern developed economies as well
as their vulnerability to endogenous instabilities. The theory of complex systems
thus explains the origin of Adam Smith's invisible hand in society according
to which a collection of selfish self-centered individuals (or countries) coldly
maximizing their individual "utility functions" achieve an optimal
aggregate social welfare. This theory explains capitalism and free trade. However,
it also explains and predicts the occurrence of instabilities and of far-from-optimal
equilibrium situations, which are inherent in the bottom-up self-organization
(Sornette, 2003).

This problem is also linked to Arrow's impossibility theorem for aggregating
individual preferences [Gaertner, 2001]. What Kenneth Arrow was able to prove
mathematically is that there is no method for constructing social preferences
from arbitrary individual preferences. In other words, there is no rule, majority
voting or otherwise, for establishing social preferences from arbitrary individual
preferences. In simple words, a consistent policy for the world, which is agreeable
to all parties, would not be possible. There is however one way out of this
impasse for making social decisions through the political process. If the individual
preferences have some commonality, then social preferences can be constructed.
This understanding suggests its remedy: a group approach, or in other words
a kind of top-down approach, recognizing the necessity of extending the standard
economic goal of individuals' utility maximization to the reality of a "social
capital" both within and across countries. Rather than focusing on individual
utilities, this could be term the group utility of society. Recent works studying
the behavior of groups, in particular the existence of altruistic behaviors,
suggest the existence of such group utility [Fehr and Gachter, 2002].

Famous economists such as P. Krugman and J.E. Stiglitz and financier G. Soros
have also emphasized the limits of free markets and the need for well-thought
regulations and interventions. This chorus the spirit of J.M. Keynes who stressed
that, at times of crises, there is a need for governments to develop a world-conscious
solidarity extending beyond the selfish interests of each individual country.
The science of complex systems provides a novel twist to these analyses by
suggesting a deeper justification that extends the bottom-up approach to a
more fundamental understanding of our societies incorporating the utility of
groups at many levels of interactions.

The transition from selfish to group utility will not be done easily and gleefully
but the torments ahead may force us to realize this is our only long-term solution.
This may actually be an opportunity to transition towards a society with a
better balance between freedom and group welfare.